Given pi/2

We notice that the angle x is located in the 2nd quadrant,
therefore the values of cotangent function are negative.

We
know that cot x = cos x/sin x

We'll determine cos x,
applying the Pythagorean identity:

(cos x)^2 + (sin x)^2 =
1

(cos x)^2 = 1 - (sin
x)^2

(cos x)^2 = 1 - 9/25

(cos
x)^2 = (25 - 9)/25

(cos x)^2 =
16/25

cos x = -4/5

We'll keep
only the negative value for cos x, since x is in the second quadrant and cosine function
is negative.

cot x =
(-4/5)/(3/5)

cot x =
-4/3

The value of cotangent function is: cot
x = -4/3.